{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:43:35Z","timestamp":1760150615200,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T00:00:00Z","timestamp":1702857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["A2020402006","11701136"],"award-info":[{"award-number":["A2020402006","11701136"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["A2020402006","11701136"],"award-info":[{"award-number":["A2020402006","11701136"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing total coloring. The neighbor distinguishing edge (total) coloring of a graph G is an edge (total) coloring with the requirement that each pair of adjacent vertices contains different color sets. The neighbor distinguishing edge (total) chromatic number of G is the smallest integer k in cases where a neighbor distinguishing edge (total) coloring exists through the use of k colors in G. The maximum average degree of G is the maximum of the average degree of its non-empty subgraphs. In this paper, we characterize the neighbor distinguishing edge (total) chromatic numbers of graphs with a maximum average degree less than four by means of the discharging method.<\/jats:p>","DOI":"10.3390\/axioms12121132","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T03:59:24Z","timestamp":1702871964000},"page":"1132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3299-6060","authenticated-orcid":false,"given":"Jingjing","family":"Huo","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China"}]},{"given":"Sensen","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China"}]},{"given":"Yulong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China"}]},{"given":"Mingchao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/S0893-9659(02)80015-5","article-title":"Adjacent strong edge coloring of graphs","volume":"15","author":"Zhang","year":"2002","journal-title":"Appl. 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